You're properly already familiar with some ways to prevent heat-related illnesses such as hydrating properly, slowing your pace in hot and humid conditions, and running in the morning or evening. But here are a couple of more ideas:
Drink something really cold before you start. A study from New Zealand found that drinking a syrup-flavored ice slushie before running on a treadmill extended runners' endurance by an average of 10 minutes. Researchers weren't certain why slushies had that effect, but one possible explanation is that the slushies lowered the runners' body temperature before they began running, allowing them to run longer before they felt the effects of the heat.
"Pre-cool" yourself. During the 2004 Summer Olympics in Athens, I remember seeing footage of U.S. marathoner Deena Kastor wearing an ice vest to lower her body temperature before she ran to a bronze medal finish in the marathon. A study showed that wearing a cooling vest before running can indeed delay the effects of heat. Of course, you probably don't own an ice vest, but it can still help to precool yourself by hanging out in a cold, air-conditioned room right before you start running.
Cool your neck. As any runner who has dumped water on the back of their neck during a hot run can tell you, keeping your neck cold helps you feel cooler. Try a cooling trick from competitors in the Badwater Ultramarathon. Lay a bandana out flat and place a row of ice cubes from one corner of the bandana to another. Then roll it up and tie it around your neck.